why does alice follow bob?lilianweng.github.io/files/shortcuts.pdf · two key ingredients a b c...

Why does Alice follow Bob?

Filippo MenczerCenter for Complex Networks and Systems Research

School of Informatics and ComputingIndiana University, Bloomington

The Role of Information Diffusion in the Evolution of

Social Networks

Marvin

trut

hy.in

dian

a.ed

u

Competition for attention

Dynamics of the network

Dynamics on the network

Dynamics of Network:Link Creation

Dynamics on Network:InforPDWLRQ�Àow

A B

A B

Dynamics of Network:Link Creation

Dynamics on Network:InforPDWLRQ�Àow

A B

A B

memepopularity(number of messages)

lifetime (longest consecutive

number of days)

#bieberfact 139760 145

#bieberthing 3 1

Two key ingredients

AB

C

DPost existing topics(1 - Pn)

Post a new topic(Pn)

#jobs

#justinbieber

#ladygaga

#apple

!#jan25

#apple

#jobs

#justinbieber

#apple

#jan25

#apple

#jobs

#jan25

#ladygaga

#jan25#jobs

#jan25#jobs

AB

C

D

Before After

Follower Post

Screen(Pr) Memory ("! Pr) Screen(Pr) Memory ("! Pr)(Pm) (Pm)

Weng et al. Nature Sci. Rep. 2012

Dataset: Twitter 10% sampleOctober 2010 – January 2011~12.5M users, ~1.3M hashtags

b

c d

NJ�Į

a

Competition for attention

Dynamics of the network

Dynamics on the network

Dynamics of Network:Link Creation

Dynamics on Network:InforPDWLRQ�Àow

A B

A B

Dynamics of Network:Link Creation

Dynamics on Network:InforPDWLRQ�Àow

A B

A B

Dynamics of Network:Link Creation

Dynamics on Network:InforPDWLRQ�Àow

A B

A B

shortcut

Dataset: Yahoo! MemeApril 2009 – March 2010

(A)

(B)

~128k users, ~3.5M links, ~7M posts

TargetUser

Information FlowFollowing(A)

(B)

4.13%

14.89%

61.46%17.24%

0.03%

0.15%

2.00%

0.10%

Others

GrandparentOriginTriadic Node

Traffic shortcut 24%

Triadic closure 85%

TargetUser

Information FlowFollowing(A)

(B)

4.13%

14.89%

61.46%17.24%

0.03%

0.15%

2.00%

0.10%

Others

GrandparentOriginTriadic Node

Traffic shortcut 24%

Triadic closure 85%

TargetUser

Information FlowFollowing(A)

(B)

4.13%

14.89%

61.46%17.24%

0.03%

0.15%

2.00%

0.10%

Others

GrandparentOriginTriadic Node

Traffic shortcut 24%

Triadic closure 85%

TargetUser

Information FlowFollowing(A)

(B)

4.13%

14.89%

61.46%17.24%

0.03%

0.15%

2.00%

0.10%

Others

GrandparentOriginTriadic Node

Traffic shortcut 24%

Triadic closure 85%

TargetUser

Information FlowFollowing(A)

(B)

4.13%

14.89%

61.46%17.24%

0.03%

0.15%

2.00%

0.10%

Others

GrandparentOriginTriadic Node

Traffic shortcut 24%

Triadic closure 85%

Could this happen by chance?

Could this happen by chance?

Actual number of links of that type in the

data

Expected number of links of a certain type according to the null hypothesis (by

chance). E.g., links to grandparents:

Could this happen by chance?

Actual number of links of that type in the

data

very large ⇒ reject null hypothesis:

links are not created randomly

Expected number of links of a certain type according to the null hypothesis (by

chance). E.g., links to grandparents:

Preference for traffic-based shortcuts as users become more active

The more messages we see from someone, the more we are likely

to follow them

Preference for traffic-based shortcuts as users become more active

The more posts we see from someone, the more

we are likely to follow them

Rank percentile (by traffic)

P

The more messages we see from someone, the more we are likely

to follow them

Preference for traffic-based shortcuts as users become more active

The more posts we see from someone, the more

we are likely to follow them

Rank percentile (by traffic)

P

The more messages we see from someone, the more we are likely

to follow them

Shortcuts are more efficient at carrying messages we see and report

1e-7 (B) Reposted Traffic

Link

effi

cien

cy

Maximum Likelihood Estimation

Maximum Likelihood Estimation

∀ link ℓ, compute:

f(ℓ | Γ, Θ) = likelihood of the target being

followed by the creator according to a particular strategy Γ, given the network

configuration Θ at the time when ℓ is created.

Maximum Likelihood Estimation

∀ link ℓ, compute:

f(ℓ | Γ, Θ) = likelihood of the target being

followed by the creator according to a particular strategy Γ, given the network

configuration Θ at the time when ℓ is created.

Single strategy

Combined strategy

Individual strategy

MLE single strategies

• Random

• Triadic closure (∆)

• Grandparent (G)

• Origin (O)

• Traffic shortcut (G ∪ O)

MLE single strategies

• Random

• Triadic closure (∆)

• Grandparent (G)

• Origin (O)

• Traffic shortcut (G ∪ O)

MLE single strategies

• Random

• Triadic closure (∆) 1–p

p

1–pp

MLE single strategies

• Random

• Triadic closure (∆)

• Grandparent (G)

1–p

p

MLE single strategies

• Random

• Triadic closure (∆)

• Grandparent (G)

• Origin (O)

• Traffic shortcut (G ∪ O)

1–p

p

MLE single strategies

• Random

• Triadic closure (∆)

• Grandparent (G)

• Origin (O)

• Traffic shortcut (G ∪ O) Example:

MLE combined strategies

• Grandparent or triadic closure (G + ∆)

• Origin or triadic closure (O + ∆)

• Traffic shortcut or triadic closure (G ∪ O + ∆)

MLE combined strategies

• Grandparent or triadic closure (G + ∆)

• Origin or triadic closure (O + ∆)

• Traffic shortcut or triadic closure (G ∪ O + ∆)

1–p1–p2

p1

p2

MLE combined strategies

• Grandparent or triadic closure (G + ∆)

• Origin or triadic closure (O + ∆)

• Traffic shortcut or triadic closure (G ∪ O + ∆)

Example:

1–p1–p2

p1

p2

MLE combined strategies

• Grandparent or triadic closure (G + ∆)

• Origin or triadic closure (O + ∆)

• Traffic shortcut or triadic closure (G ∪ O + ∆)

Example:

1–p1–p2

p1

p2

Maximum Likelihood(G ∪ O + ∆)

p(traffic shortcut)

p(∆)

p(traffic shortcut)

p(∆)

4.7%

Maximum Likelihood(G ∪ O + ∆)

=1.0

= 0.0( ) =1.0=1.0

= 0.0

(

)

= 0.

0

(

)

Random BrowsingMixtureInformation-OrientedCasual FriendshipFrienship

10.4%

4.7%28%51% 5.5%

=1.0

= 0.0( ) =1.0=1.0

= 0.0

(

)

= 0.

0

(

)

Random BrowsingMixtureInformation-OrientedCasual FriendshipFrienship

10.4%

4.7%28%51% 5.5%

4.7%

(A) (B) (C)

(F) In-degree ratio(D) Lifetime (E) In-degree

(H) Posts (I) Post ratio(G) Reposted

longer lived follow more more followers

influential active spreaders

As users become more active, more popular, and more influential, they make the network more “efficient” by shortening the distance between producers and consumers of information.

Papers: cnets.indiana.edu/groups/nan/truthy